Moir\'e Assisted Fractional Quantum Hall State Spectroscopy

Abstract

Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moir\'e pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moir\'e-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on $f-$sum rule considerations supplemented by a perturbative analysis of the influence of the moir\'e potential on many-body states.